Education Secretary Arne Duncan has jumped into the food fight over school breakfast, calling for schools nationwide to adopt new programs to provide free morning meals, which Mayor Bloomberg’s administration warns might lead city kids to pack on the pounds.

Duncan wants schools to offer programs that provide breakfast to all kids — rather than making poor kids show up at the school cafeteria early — to avoid any social “stigma.”

He also backs “Grab ’N’ Go” meals and other federally funded programs to let kids eat in their classrooms each morning.

“I am encouraging schools, school administrators and teachers to seek out these and other innovative ways to increase participation in the school-breakfast program,” Duncan wrote in a letter to school officials nationwide in a letter last week, in keeping with a City Council resolution passed this year supporting classroom breakfasts. But the weight-watching Bloomberg administration has been critical.

“I am concerned that if we have breakfast in every classroom, that that could contribute to the problem [of child obesity] and possibly make it worse,” Dr. Thomas Farley, a Health Department commissioner, testified at a City Council hearing this year.

“Our administration has made free breakfast available to each of our 1.1 million students every morning, and has . . . empowered principals to decide if their schools should offer Breakfast in the Classroom,” said Bloomberg spokeswoman Lauren Passalacqua, declining to endorse Duncan’s call for universal breakfast.